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If A+B+C= 180^(@), then show that sin 2...

If `A+B+C= 180^(@)`, then show that ` sin 2A+ sin 2B+ sin 2C =4 sin A sin B sin C`.

A

`sin A sin B sin C `

B

`4 sin A sin B sin C `

C

`3 sin A sin B sin C`

D

`2 sin A sin B sin C `

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If A+B+C= 180^(@) , " then " ( sin 2A- sin 2B- sin 2C)/(sin 2B- sin 2A - sin 2C)=

    A
    `tan A* cot B `
    B
    `cot A * tan B`
    C
    `2 tanA * cot B `
    D
    `2 cot A * tan B `

  • In DeltaABC,(sin 2A+ sin 2B+ sin 2C)/(sin A + sin B+ sin C)=

    A
    `4 sin""(A)/(2) sin""(B)/(2) sin""(C)/(2) `
    B
    `4 cos""(A)/(2) cos""(B)/(2) cos""(C)/(2)`
    C
    `8sin""(A)/(2)sin""(B)/(2)""sin""(C)/(2)`
    D
    `1+4 sin""(A)/(2)sin""(B)/2 sin""(C)/(2)`

  • If A+B+C= 90^(@) " then " sin 2A+ sin 2B- sin 2C=

    A
    `1+ 4 sin A sin B sin C `
    B
    `1-2 sin A sin B sin C `
    C
    `2+ 2 sin A sin B sin C `
    D
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    Explore conceptually related problems

    If A+B+C=180^@ , then show that sin2A+sin2B+sin2C=4sinAsinBsinC .

    If A+B+C=270^(@) then show that sin2A+sin2B-sin2C=-4sinAsinBcosC

    If A+B+C=(pi)/(2) , then prove that cos 2A + cos 2B + cos 2C=1+4 sin A sin B sin C .

    If A+B+C=90^(@) then prove that sin2A+sin2B+sin2C=4cosAcosBcosC

    Prove that a cos A + b cos B + c cos C = 4 R sin A sin B sin C .

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